Abstract
Let \(I \subseteq \mathbb{R}\) be an interval. We say that a function \(f: I \rightarrow \mathbb{R}\) has the intermediate value property (or IVP, for short) if it takes all intermediate values between any two of its values. More precisely, for every a, b ∈ I and for any λ between f(a) and f(b), we can find c between a and b such that f(c) = λ. A direct consequence of this definition is that f has IVP if and only if it transforms any interval into an interval. Equivalently, a function with IVP which takes values of opposite signs must vanish at some point.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Science+Business Media LLC
About this chapter
Cite this chapter
Andreescu, T., Mortici, C., Tetiva, M. (2017). The Intermediate Value Theorem. In: Mathematical Bridges. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4629-5_11
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4629-5_11
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-0-8176-4394-2
Online ISBN: 978-0-8176-4629-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)